IGCSE Physics 0625: Friction, Drag and Resultant Force on a Cyclist

A cyclist rides her bicycle along a flat, straight road.

(a) State the name of two different resistive forces that act on the cyclist and bicycle as she rides along, and briefly state what causes each one. [2]

(b) The cyclist's brakes work by pressing rubber brake blocks against the wheel rims. Describe, in terms of friction, the effect this contact has on the motion of the wheel, and describe one other effect this friction has on the brake blocks and wheel rims themselves. [2]

(c) While cycling, the cyclist pedals so that the forward driving force from the wheels is exactly balanced by the total resistive force acting on her. State what this tells you about her speed, and explain your answer by referring to the resultant force and Newton's first law. [2]

(d) The cyclist then pedals harder so that the forward driving force increases to $230\text{ N}$ , while the total resistive force stays at $205\text{ N}$ . Calculate the resultant force now acting on the cyclist and bicycle, and state the effect this has on her speed. [2]

Part (a): Resistive forces on the cyclist

Two different resistive forces act on a moving cyclist:

Air resistance (drag), caused by the cyclist and bicycle pushing through the air.
Friction, caused by solid surfaces rubbing together in the moving parts of the bicycle, for example the chain, the wheel bearings, and the tyres in contact with the road.

Part (b): Friction at the brakes

When the brake blocks are pressed against the wheel rim, the friction between the two surfaces impedes (opposes) the rotation of the wheel, which is exactly why the brakes slow the bicycle down.

This friction also produces heating: the brake blocks and wheel rims get noticeably warmer after braking, because some of the bicycle’s kinetic energy is transferred to internal (thermal) energy in these surfaces.

Part (c): Balanced forces and constant speed

If the forward driving force is exactly balanced by the total resistive force, then:

$\text{Resultant force} = \text{driving force} - \text{resistive force} = 0$

By Newton’s first law, an object continues at rest, or continues moving in a straight line at a constant speed, unless a resultant force acts on it. Since the resultant force here is zero, the cyclist’s velocity does not change, she travels at a constant velocity.

Part (d): Pedalling harder

The driving force and resistive force now act in opposite directions along the same line, so subtract to find the resultant:

$\text{Resultant force} = 230\text{ N} - 205\text{ N} = \boxed{25\text{ N}}$

This resultant force of $25\text{ N}$ acts forward, in the same direction the cyclist is already travelling. An unbalanced force acting in the direction of motion increases her speed, so the cyclist speeds up (accelerates).

Final answers

(a) Air resistance (from moving through the air) and friction (from solid surfaces rubbing together, e.g. chain and bearings)
(b) Friction impedes the wheel’s rotation and produces heating at the brake blocks and rim
(c) She moves at a constant velocity, because the resultant force is zero (Newton’s first law)
(d) Resultant force $=$ $25\text{ N}$ forward; the cyclist speeds up